Box and Whisker Plots and the 5 number summary

Mr. J.D. Miles

Turner Middle School

Atlanta Georgia

milesmath@gmail.com

www.JovanMiles.com

The 5 Number Summary

• The five number summary is another name for the visual representation of the box and whisker plot.

• The five number summary consist of : The median ( 2nd quartile) The 1st quartile (lower quartile) LQ The 3rd quartile (upper quartile) UQ The maximum value in a data set (upper

extreme) UE The minimum value in a data set (lower extreme)

LE

Constructing a box and whisker plot

• Step 1 - Find the median.

• Arrange the numbers in order from least to greatest.

• Remember, the median is the middle value in a data set.

18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100

68 is the median of this data set.

Constructing a box and whisker plot

• Step 2 – Find the lower quartile.

• The lower quartile is the median of the data set to the left of 68. (lower part of data set)

(18, 27, 34, 52, 54, 59, 61,) 68, 78, 82, 85, 87, 91, 93, 100

52 is the lower quartile

Constructing a box and whisker plot

• Step 3 – Find the upper quartile.

• The upper quartile is the median of the data set to the right of 68. (the upper part of the data set)

18, 27, 34, 52, 54, 59, 61, 68, (78, 82, 85, 87, 91, 93, 100)

87 is the upper quartile

Constructing a box and whisker plot

• Step 4 – Find the maximum and minimum values in the set.

• The maximum is the greatest value in the data set. (Upper Extreme) UE

• The minimum is the least value in the data set. (Lower Extreme) LE

18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100

18 is the minimum and 100 is the maximum.

Constructing a box and whisker plot

• Step 5 – Find the inter-quartile range (IQR).

• The inter-quartile (IQR) range is the difference between the upper and lower quartiles. Upper Quartile = 87 Lower Quartile = 52 87 – 52 = 35 35 = IQR

The 5 Number Summary

• Organize the 5 number summary Median – 68 Lower Quartile – 52 Upper Quartile – 87 Max (Upper Extreme) UE – 100 Min (Lower Extreme) LE – 18

Create a NUMBER LINE using your data…. Plot the 5 points on the number line. Draw a BOX around LQ and UQ Draw a LINE thru MEDIAN. Connect the LE and UE to the BOX as WHISKERS.

Graphing The Data

• Notice, the Box includes the lower quartile, median, and upper quartile.

• The Whiskers extend from the Box to the max and min.

Analyzing The Graph

• The data values found inside the box represent the middle half ( 50%) of the data.

The lower extreme to the lower quartile is 25% of the data.

The lower quartile to the median is 25% of the data.

The median to the upper quartile is 25% of the data.

The upper quartile to the upper extreme is 25% of the data.

Practice

• Use the following set of data to create the 5 number summary.

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

Median

• What is the median or 2nd quartile?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

• The median is 39

Lower Quartile ( 1st Quartile )

• What is the lower or 1st quartile?

(3, 7, 11, 11, 15, 21, 23), 39, 41, 45, 50, 61, 87, 99, 220

• The lower quartile is 11

Upper Quartile ( 3rd Quartile )

• What is the upper or 3rd quartile?

3, 7, 11, 11, 15, 21, 23, 39, (41, 45, 50, 61, 87, 99, 220)

• The upper quartile is 61

Maximum

• What is the maximum?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

• The max is 220

Minimum

• What is the minimum?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

• The min is 3

The 5 Number Summary

• Median - 39

• Lower Quartile - 11

• Upper Quartile - 61

• Max - 220

• Min - 3

Graphing The Data

Take out your graph paper so we can practice graphing the data.

Box and Whisker Plots and the 5 number summary

Mr. J.D. Miles

Turner Middle School

Atlanta Georgia

www.JovanMiles.com